Determining calibrated measurements of pressure for different sensors

ABSTRACT

Systems and methods for calibrating individual pressure sensors using mathematical models to compensate for inaccurate measurements of pressure from those pressure sensors are described. Also described are systems and methods for applying those mathematical models to adjust measurements from those pressure sensors during position computations.

FIELD

This disclosure relates generally to positioning systems. Morespecifically, but not exclusively, the disclosure relates to systems andmethods for determining calibration models associated with differentsensors, and for using those calibration models to compute positions ofthe sensors.

BACKGROUND

Positioning systems and methods like those used in relation to satelliteor terrestrial transmitter networks have been widely used to determineposition information for mobile computing devices like smart phones.However, many of these systems and methods do not deliver the accuracyneeded to determine an exact location of the device. For instance, ifthe device is in a multi-story building, not knowing the floor oraltitude at which the device resides will result in delays in providingemergency assistance, which could be potentially life-threatening. Asdescribed in U.S. patent application Ser. No. 13/296,067 (filed Nov. 14,2011), techniques for estimating an altitude of a device may usemeasurements of pressure at the device. These measurements may beobtained from low-cost MEMS sensors that are incorporated into thedevice. In many cases, these low-cost MEMS sensors have precision thatis comparable to calibration instruments, but the sensors providemeasurements that lack accuracy needed for reliable altitudecomputations.

Many pressure sensors, for example, provide measurements with errorsthat could result in an estimated altitude of a device that differs fromthe device's actual location by two or more floors. This reducedaccuracy is unacceptable in various situations, including emergencyresponse activities that rely on floor-level accuracy to reach users asquickly as possible. Thus, sensors ideally must be calibrated to reducesuch error.

Unfortunately, the same amount of calibration cannot be used for eachsensor, since sensors of the same model that are manufactured by thesame manufacturer often provide different measurements of the sameenvironmental condition (e.g., atmospheric pressure). Consequently,different calibration is often needed on a sensor-by-sensor basis.

To make matters more complicated, a single sensor may performdifferently under different environmental conditions. For example,different levels of temperature may affect the performance of a pressuresensor. As a consequence, different calibration may be needed for thesame sensor depending on environmental conditions.

Clearly, systems and methods that determine how to calibrate a pressuresensor and that use the calibration(s) would improve estimations of thesensor's altitude. Fortunately, this disclosure describes variousembodiments of such systems and methods, which are also useful for othertypes of sensors beyond pressure sensors.

SUMMARY

This disclosure relates generally to positioning systems. Morespecifically, but not exclusively, the disclosure relates to systems(networks, devices, or components), methods, means, and machine-readablemedia embodying program instructions adapted to be executed by systemsto implement methods for determining calibration models associated withdifferent sensors, and for using those calibration models.

Some aspects of the disclosure relate to calibration systems and methodsthat are configured to identify operating parameters of a sensor like atemperature range and a pressure range. The calibration systems andmethods may be further configured to, for each of a plurality ofdifferent temperature and pressure combinations within the operatingparameters, identify reported measurements of pressure from a sensorwhen the sensor is stabilized to each combination of temperature and thepressure; and compute a pressure measurement error based on a comparisonof a calibrated measurement of the pressure and the reportedmeasurement. The calibration systems and methods may also oralternatively be configured to select a mathematical model thatsufficiently fits the computed pressure measurement errors as a functionof the reported measurement of pressure and a measurement oftemperature, and store a pressure measurement error function based onthe mathematical model for later use in adjusting pressure measurementsfrom the sensor.

Additional aspects of the disclosure relate to systems and methods thatare configured to use the pressure measurement error function toestimate a pressure measurement error associated with a measuredpressure by the sensor during its use in a mobile computing device. Thesystems and methods may then adjust the measured pressure by thepressure measurement error to obtain an adjusted pressure measurementfor use in determining an altitude of the sensor.

Additional aspects are described below in conjunction with the Drawings,Detailed Description and Claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a positioning network.

FIG. 2 depicts a transmitter.

FIG. 3 depicts a user device.

FIG. 4 depicts a calibration system for determining how to calibrate asensor by estimating measurement error associated with a pressuresensor.

FIG. 5 illustrates a process for generating a function that estimatesmeasurement error associated with a type of sensor under variousoperational conditions.

FIG. 6 illustrates a process for generating a function that estimatesmeasurement error associated with a pressure sensor under variousoperational conditions associated with temperature and pressure.

FIG. 7 shows a plot of observed pressure measurement errors at differentcombinations of temperature and pressure.

FIG. 8 shows a plot of a mathematical model's fit to observed pressuremeasurement error.

FIG. 9 shows a plot of residual error associated with observed pressuremeasurement errors and estimated pressure measurement errors.

DETAILED DESCRIPTION Example Systems

FIG. 1 depicts a positioning network 100 on which various embodimentsmay be implemented. The positioning network 100 includes a network ofsynchronized transmitters 110 (also denoted herein as “beacons” or“towers”), which are depicted as terrestrial, as well any number of userdevices 120 configured to acquire and track signals provided from thetransmitters 110, satellites 150, and/or another terrestrial node 160.The user device 120 may include a location computation engine (notshown) to determine position information based on the signals receivedfrom the transmitters 110. The network 100 may further include a serversystem 130 that includes a processor and database, and that is incommunication with various other systems, such as the transmitters 110,the user devices 120, and one or more network infrastructures 170 (e.g.,the Internet, other networks). Three user devices 120 a-c are depictedat various altitudes; however, the network 100 would typically beconfigured to support more user devices 120 at more altitudes within adefined coverage area. The user devices 120 may receive/send signalingvia communication links 113, 153 and 163.

Transmitters

Details of one embodiment of the transmitter 110 are shown in FIG. 2. Asshown, the transmitter 200 sends, receives and processes signals via anRF component 230. Memory 220 may be coupled to a processor 210 toprovide storage and retrieval of instructions relating to describedmethods that may be executed by the processor 210. The transmitter 200includes one or more environmental sensors 270 for measuringenvironmental conditions like pressure, temperature, humidity, and/orother environmental conditions. As described later, measured conditionscan be used to estimate an altitude of the user device 120 so long asthe measurements by the sensors 270, along with measurements by sensorsat the user device 120, are accurate.

User Device

Details of one embodiment of the user device 120 are shown in FIG. 3. Asshown, the user device 300 sends, receives and processes signals via anRF component 330. Memory 320 may be coupled to a processor 310 toprovide storage and retrieval of instructions relating to describedmethods that may be executed by the processor 310. Inputs/outputs 390are provided to receive input from a user and to provide output to theuser.

The user device 300 also includes one or more environmental sensors 370for measuring environmental conditions like pressure, temperature,humidity, acceleration, direction of travel, and/or other conditions.Pressure measured by the environmental sensors 370, along with pressuremeasured by the transmitter 200, may be used by the processor 310 toestimate an altitude of the user device 300.

Various methods for using pressure to estimate an altitude of a userdevice 120 are disclosed in co-owned U.S. patent application Ser. No.13/296,067, filed Nov. 14, 2011. For example, atmospheric pressure isrelated to elevation by a hypsometric equation:

${{z_{2} - z_{1}} = {\frac{RT}{g}{\ln ( \frac{p_{1}}{p_{2}} )}}},$

where p₁ is the atmospheric pressure at the elevation z₁, and p₂ is theatmospheric pressure at elevation z₂. R is the gas constant of air, T isthe temperature, and g is the acceleration due to gravity. Thus, if theair temperature is known, and the sea level pressure, p₁, is known, onecan set z₁ to zero and compute the elevation z₂ above sea level, whichcorresponds to any measured pressure p₂. This formulation assumes thatthe temperature does not vary with elevation.

A barometric formula assumes that the temperature decreases linearlywith elevation:

${p = {p_{0}( {1 - \frac{Lh}{T_{0}}} )}^{\frac{g}{RL}}},$

where p is the pressure at an elevation h, given the pressure andtemperature at sea level, p₀ and T₀, and the lapse rate L (change intemperature per unit height). The above and other equations may be usedto compute an estimate of a sensor's altitude.

One of ordinary skill in the art will appreciate that accurate pressureand temperature measurements by sensors at the transmitter 200 and theuser device 300 are necessary for an accurate altitude computation.Thus, there is a need to calibrate at least the pressure sensor at theuser device 300, and possibly the pressure sensor at the transmitter200. Fortunately, this disclosure describes processes for calibratingpressure sensors.

Calibrating Sensors

In order to better understand various aspects of this disclosure, it isnoted that sensors used in user devices 120 may not always outputaccurate measurements. In some cases, the measurements may not besufficiently accurate for the intended use of the measurements.

It is also noted that two sensors of the same model, and manufacturedunder nearly identical circumstances, may output different measurementsunder the same environmental conditions. For example, two such pressuresensors, when occupying nearly the same location in a building at thesame time, may measure different pressures.

In order to estimate the pressure at a location of a user device 120with sufficient accuracy, it is important to estimate the differencebetween the actual pressure at that location and the measurement of thatpressure by a pressure sensor of the user device 120. If the differencebetween actual pressure and measured pressure can be estimated withsufficient accuracy, then a more-accurate assessment of the pressure canbe made by increasing or decreasing the pressure measurement using theestimated difference. This more-accurate assessment of the pressure canbe used to estimate the altitude of the user device with more accuracyas compared to using the unadjusted measurement of pressure from thepressure sensor. By comparison, the measurement of the pressure by thepressure sensor may fall within 200 Pa of the actual pressure, and themore-accurate assessment of the pressure may fall within 50 Pa or even10 Pa of the actual pressure.

One approach for estimating the difference between actual pressure andmeasured pressure uses a mathematical model of the difference betweenactual and measured pressures as a function of temperature and pressure.The mathematical model may be based on comparisons of actual pressure tomeasured pressure when the pressure sensor is stabilized to differentcombinations of temperature and pressure that are selected from a rangeof temperatures and a range of pressures. The number of combinations mayvary depending on the level of accuracy desired when applying themathematical model.

FIG. 4 depicts a calibration system 400 for generating such amathematical model that estimates pressure measurement error associatedwith a particular pressure sensor. The system 400 includes anenvironment 401 within which different temperatures (1-m) and differentpressures (1-n) are inputted. A pressure sensor 370 a and a temperaturesensor 370 b are shown as integrated into a user device 300. It is to beunderstood that the sensors 370 a and 370 b may alternatively be testedwithin environment 401 without being integrated into the user device300, and the sensors 370 a and 370 b may be integral to each other,coupled to each other, or independent of each other.

As shown, the environment 401 may include the pressure sensor 370 a, thetemperature sensor 370 b, and a calibration instrument 402 that iscapable of measuring pressure with desired accuracy. Alternatively,another calibration instrument (not shown) that is capable of measuringtemperature with desired accuracy may be used along with, or instead ofthe temperature pressure sensor 370 b when the temperature sensor 370 bis known to output temperature measurements that are within a toleratederror from true temperature.

Measurements from each of the pressure sensor 370 a, the temperaturesensor 370 b, and the calibration instrument 402 may be output, storedby a data source 404, and used by a processor 405 to perform variousmethods described herein, including the methods described below inrelation to FIG. 5 and FIG. 6. Different measurements from the pressuresensor 370 a, the temperature sensor 370 b, and the calibrationinstrument 402 may be output depending on the number of adjustments madeto the temperature and pressure within the environment 401.

Attention is now turned to FIG. 5, which illustrates a process forgenerating a mathematical model that estimates measurement errorassociated with a particular sensor (e.g., sensor 370 a). The process ofFIG. 5 may be used for a sensor of any type (e.g., sensors that measurepressure, temperature, humidity, motion, vibration, direction, light,air movement, time, proximity to other things, and other conditions).Examples, however, are provided in relation to pressure sensors;however, these examples should in no way limit the disclosure of theprocess in FIG. 5 to a pressure sensor.

As illustrated in FIG. 5, operating parameters associated with expectedoperating conditions of the sensor are identified (501). The operatingparameters identify environmental variables under which the sensor mayoperate. For example, sets or ranges of temperature and pressure may bespecified.

Other variables are contemplated for other implementations of the methodin FIG. 5, including humidity, vibration applied to the sensor, windvelocity, ambient light, and age of a sensor. Correlation between eachof variables and accurate sensor measurements are contemplated where thecorrelated relationship can be used to determine adjustments to sensormeasurements. For example, aging of a sensor or vibration on a sensor,as those conditions affect a pressure measurement accuracy of thesensor, can be recorded and used to adjust pressure measurements basedon the age of the sensor or a vibrational input (e.g., from anaccelerometer) during operation of the sensor.

Any set or range may be determined based on expected operatingconditions of the sensor while in use by a user. For example, a range oftemperatures and a range of pressures may be determined by minimum andmaximum temperatures and pressures a typical user will experience whileoperating the pressure sensor.

Multiple combinations of the operating parameters are identified (502)from the ranges of temperature and pressure. The sensor may then operateunder each combination of the operating parameters, during which one ormore recorded values of measurements from the sensor are stored.

Each measurement may be compared to a corresponding measurement taken bya calibration instrument (e.g., the calibration instrument 402). Duringthe comparison of the measurements, the difference between each of thesensor's measurements and corresponding measurements made by thecalibration instrument is determined. This difference represents anobserved error of the sensor's measurement (503). For example, thepressure sensor 370 a may operate under different combinations oftemperature and pressure, and measurements of pressure by the pressuresensor 370 a may be compared to corresponding measurements from thecalibration instrument 402.

A measurement corresponding to the other initial parameter may also berecorded with respect to each combination of the operating parameters.For example, the temperature sensor 370 b may also operate under thedifferent combinations of temperature and pressure, and measurements oftemperature by the temperature sensor 370 b may be associated with acorresponding pressure measurement and observed error of the pressuremeasurement.

Once a set of observed errors is determined, one or more mathematicalmodels may be generated to fit the observed errors as a function of therecorded values. Possible mathematical models include polynomial,trigonometric, spline, exponential, and other mathematical modelfamilies. Other models may include dividing the ranges of operatingparameters into smaller sub-ranges, and then using differentmathematical models in different sub-ranges, or applying a firstmathematical model and then using a second mathematical model to modelthe residual error of the first mathematical model after it is appliedto one or more combinations of operating parameters.

A mathematical model may be selected based on different considerations(504). For example, the model that best fits the observed errors may beselected. Alternatively, a model with a minimum amount of residuals thatmeet a threshold condition (e.g., are less than 10 Pa, 20 Pa, 50 Pa, oranother amount) may be selected. The minimum amount may be specified by:a predefined percentage of all residuals; a total of all residualswithin sub-ranges of the operating parameters; a higher percentage ofresiduals as compared to a corresponding percentage of residuals foranother mathematical model; or other approaches for specifying theminimum amount. Alternatively, an average of residuals may be requiredto meet the threshold condition above. In addition, it may be requiredthat the largest residual of the averaged residuals falls below anotherthreshold value.

Once a suitable mathematical model is selected, an offset associatedwith modeled error and observed error may be determined. In oneimplementation, an additional measurement is taken from the sensorduring its operation under a combination of the operating parameters.The sensor's measurement of a first parameter and a measurement of thesecond parameter may be used as inputs for the mathematical model toproduce the modeled error (505). The sensor measurement of the firstparameter is compared to an accurate measurement of the first parameter,and a difference between the sensor measurement and the accuratemeasurement is computed to determine the observed error (506). Theoffset may then be determined based on the difference between themodeled error and the observed error (507).

Optionally, the process of determining an offset may be repeated underother combinations of operating parameters to produce correspondingoffsets. All of the offsets may then be used to determine a final offsetvalue. The final offset value may be an average, weighted average, orother combination of the individual offsets (or a sub-set of theoffsets) depending on the individual combinations tested.

Once a final offset is determined, an error function may be developedbased on the mathematical model and the offset (508). In oneimplementation, the offset is added to the zero order term of themathematical model.

Of course, the error function may be based on the mathematical model,but not the offset. In one implementation, a lookup table may be used toidentify an offset depending on measurements from one or moresensors—e.g., pressure and/or temperature during operation of pressureand/or temperature sensors. That offset may then be used to determine amore-accurate sensor measurement. Such an adjustment to the measurementmay be made to the initial measurement before the error function isapplied to that offset-adjusted measurement. Alternatively, the errorfunction may be applied to the initial measurement to determine anerror-function-adjusted measurement, and then the offset may be appliedto that error-function-adjusted measurement.

It is noted that the error function may use different offsets dependingon different inputs into the function (e.g., temperatures within asub-range of temperatures, pressures within a sub-range of pressures).

The previous examples related to FIG. 5 involving temperature andpressure as evaluated parameters should also in no way limit thedisclosure to two evaluated parameters. It is contemplated that anynumber of parameters can be evaluated, including one parameter, or morethan two parameters. Measurements for a corresponding number of sensorsare contemplated, including one sensor for one parameter of evaluation,three sensors for three parameters of evaluation, and so on.

Calibrating Pressure Sensor

Attention is now drawn to FIG. 6, which illustrates a process forgenerating a mathematical model that estimates pressure measurementerror associated with a pressure sensor 370 a under various operationalconditions.

Initially, temperature and pressure ranges are identified for anexpected use of the sensor (601). The expected use may define typical,expected or possible operating temperatures and pressures for thepressure sensor 370 a when integrated into a user device 300. In oneimplementation, the environmental conditions include a pressure range of72,000-107,000 Pa, and a temperature range of 0-60° C. The temperaturerange spans 0-60° C. when expected ambient operating temperatures are0-40° C. and expected internal operating temperatures of a user device300 exceed ambient operating temperature by up to 20° C.

A group of different temperature and pressure combinations are alsoidentified (602). The combinations may be spaced by 10° C. increments intemperature and 5,000 Pa increments in pressure. Thus, there could beseven temperature steps and eight pressure steps, which result in 56combinations of temperature and pressure. Alternative increments arepossible depending on the number of test combinations desired and theranges of temperature and pressure tested. In regions where error variesslowly, some combinations may be omitted from analysis of the ranges orwithin sub-ranges of temperature and pressure. In regions where theerror varies rapidly, additional combinations may be inserted across theranges or within sub-ranges of temperature and pressure. Thecombinations may form a grid of temperature (T) and pressure (P)combinations.

As shown by steps 603-607 of FIG. 6, the pressure sensor 370 a and thetemperature sensor 370 b may be stabilized to each of the combinationsof temperature and pressure, at which reported measurements may beobtained from the pressure sensor 370 a and the temperature sensor 370b. The calibration instrument 402 may also provide an accuratemeasurement of the pressure. An accurate measurement of the temperaturemay optionally be determined. The difference between the reportedmeasurement of pressure and the accurate measurement of pressure maythen determine the observed error of the reported pressure measurementfor each of the combinations of temperature and pressure. By way ofexample, FIG. 7 shows a plot of observed pressure measurement errors atdifferent combinations of temperature and pressure. The observed errorsand reported measurements of pressure and temperature are stored (608).Multiple measurements can be made at different times for the samecombinations, and those measurements may be averaged or otherwisecombined.

A mathematical model is then selected to fit the observed error as afunction of reported pressure and temperature (609). Coefficients forthe model that provide the best fit to error as a function oftemperature and pressure are determined (610), and residual errors arecomputed after the model is subtracted (611). If the values of residualsare not desired (612), a new mathematical model is selected (613), andsteps 610-612 are repeated for that new mathematical model.

By way of example, FIG. 8 shows a plot of a mathematical model's fit tothe observed pressure measurement error. By way of example, themathematical model may include a third order polynomial model whereinthe observed error (E) is given by:

E = a × p³ + b × t × p² + c × p × t² + d × t³ + e × p² + f × p × t + g × t² + h × p + i × t + j

where t and p are temperature and pressure, and a through j areconstants that are determined to provide the best fit of observed errorto the reported measurements.

By way of example, another mathematical model may include a third orderpolynomial model wherein the observed error (E) is given by:

E = a × (p − p₀)³ + b × (t − t₀) × (p − p₀)² + c × (p − p₀) × (t − t₀)² + d × (t − t₀)³ + e × (p − p₀)² + f × (p − p₀) × (t − t₀) + g × (t − t₀)² + h × (p − p₀) + i × (t − t₀) + j

where (t−t₀) and (p−p₀) are the measured temperatures and pressuresoffset by a constant temperature t₀ and a constant pressure p₀,respectively, and a through j are constants that are determined toprovide the best fit of observed error to the reported measurements. t₀and p₀ are selected to aid in the fitting of the mathematical model.

If the polynomial model does not provide a desired fit, differentpolynomial coefficients may be used for different regions of the overalltemperature-pressure test space. For example, one set of coefficientsfor temperatures above 0° C. and a different set of coefficients fortemperatures below 0° C. may be used. Alternatively, differentmathematical models may be used for different temperatures.

A particular mathematical model may be selected when its residuals meeta threshold condition. Examples of threshold conditions in relation to aminimum amount of residuals have been described previously.

By way of example, FIG. 9 shows a plot of residual error associated withthe difference between the observed value and estimated value of errorat each of the combinations of reported pressure and temperature.

Once a mathematical model is selected, the pressure sensor 370 a and thetemperature sensor 370 b are stabilized to a control temperature andpressure (614). The control temperature may be within x % (e.g., 10%) ofstandard room temperature (˜21-23 degrees C.), or typical internaloperating temperature of the user device 300 in a room temperatureenvironment. Reported pressure and temperature measurements from thepressure and temperature sensors 370 a and 370 b, an accuratemeasurement of pressure from the calibration instrument 402, and(optionally) an accurate measurement of the temperature, are recordedfor the control temperature and pressure. The observed error of thepressure sensor 370 a is determined based on the difference between thereported measurement and the accurate measurement of pressure (615). Amodeled error is also determined by inputting the reported measurementsinto the mathematical model (616). The observed error and modeled errorare then compared to determine an offset based on the difference betweenthe observed and modeled errors (617).

Alternatively, a previously measured temperature and pressure may beused instead of the control temperature and pressure to determine theoffset.

The offset, along with the mathematical model, are then stored as modelparameters for future use in adjusting measurements from the sensor 370a (618). The storage may occur at the data source 404 of FIG. 4, theserver system 130 of FIG. 1, the memory 320 of the user device 300 ofFIG. 3, or another component.

The model parameters may be accessed by a processor when computing analtitude of the user device 300 based on a measurement of pressure fromthe pressure sensor 370 a. Such a processor may include the processor310 of the user device 300, a processing component of the server system130, or another processing component.

The model parameters may define a pressure measurement error functionthat can be used to estimate the measurement error from the pressuresensor 370 a under particular environmental conditions. The estimatederror may be added or subtracted from the reported pressure measurementto obtain a more accurate estimate of true pressure.

One of skill in the art will readily extend the discussion hereinregarding pressure sensors to other sensors, including temperature,humidity, and any other sensor known or later-developed in the art.

One of skill will also recognize that similar, but differentcombinations of operating parameters may be used during differentimplementations of the calibration process, depending on the appropriateenvironment for the sensor operation. For example, during oneapplication of the calibration process, a temperature of 30° C. may beused with pressures of 72,000 Pa, 81,000 Pa, and 100,000 Pa. Duringanother implementation of the calibration process, a temperature of 32°C. may be used with those same pressures or slightly differentpressures. During yet another implementation of the calibration process,a temperature of 30° C. may be used with slightly different pressuresthan 72,000 Pa, 81,000 Pa, and 100,000 Pa. However, varying thecombinations across different implementation of the calibration processcorresponding to different sensors is acceptable since the objective isto individually test different sensors. It is also contemplated thatmultiple implementations of the calibration process may be performed onthe same sensor, and the resultant mathematical models may be comparedto select the best function, or each result from the functions may beaveraged or otherwise combined to improve the more-accurate assessmentof the sensor's measurement.

It is also contemplated that calibration may occur using historical datawhere accurate measurements of an environmental condition may becompared to measurements of that environmental condition by a sensorduring the same time or close in time. It is further contemplated thatmeasurements of an environmental condition (e.g., pressure) by a sensorand calibration device may not occur at the same location (e.g., for thepurpose of determining an offset), but rather two locations with similarlevels of the environmental condition.

Additional Embodiments of Systems and Methods

Functionality and operation disclosed herein may be embodied as one ormore methods implemented, in whole or in part, by machine(s)—e.g.,processor(s), computers, or other suitable means known in the art—at oneor more locations, which enhances the functionality of those machines,as well as computing devices that incorporate those machines.Non-transitory machine-readable media embodying program instructionsadapted to be executed to implement the method(s) are also contemplated.Execution of the program instructions by one or more processors causethe processors to carry out the method(s).

It is noted that method steps described herein may be order independent,and can therefore be performed in an order different from thatdescribed. It is also noted that different method steps described hereincan be combined to form any number of methods, as would be understood byone of skill in the art. It is further noted that any two or more stepsdescribed herein may be performed at the same time.

By way of example, method(s) and processor(s) may: identify operatingparameters, wherein the operating parameters include a temperature rangeand a pressure range.

By way of example, method(s) and processor(s) may also or alternatively:for each of a plurality of different temperature and pressurecombinations that use temperatures within the temperature range andpressures within the pressure range, identify a reported measurement ofpressure from a first sensor when the first sensor is stabilized to thetemperature and the pressure of that combination, and compute a pressuremeasurement error based on a comparison of a calibrated measurement ofthe pressure and the reported measurement.

By way of example, method(s) and processor(s) may also or alternatively:select a mathematical model, from a plurality of mathematical models,that sufficiently fits the computed pressure measurement errors as afunction of the reported measurement of pressure and a measurement oftemperature corresponding to each of the temperature and pressurecombinations.

By way of example, method(s) and processor(s) may also or alternatively:store a pressure measurement error function based on the mathematicalmodel for later use in calibrating pressure measurements from the firstsensor.

By way of example, method(s) and processor(s) may also or alternatively:identify an additional reported measurement of pressure from the firstsensor when the first sensor is stabilized to a control temperature anda control pressure.

By way of example, method(s) and processor(s) may also or alternatively:compute a control pressure measurement error based on a comparison ofthe additional reported measurement and a calibrated measurement of thecontrol pressure.

By way of example, method(s) and processor(s) may also or alternatively:compute a modeled pressure measurement error based on the mathematicalmodel using model inputs that are based on the reported measurement ofthe control pressure from the first sensor and a measurement of thecontrol temperature.

By way of example, method(s) and processor(s) may also or alternatively:determine a pressure measurement error offset based on a differencebetween the modeled pressure measurement error and the control pressuremeasurement error.

By way of example, method(s) and processor(s) may also or alternatively:store the pressure measurement error function based further on thepressure measurement error offset.

In accordance with some aspects, the control temperature is within 10%of a twenty-five degrees Celsius.

In accordance with some aspects, the plurality of different temperatureand pressure combinations are selected so that any reported pressuremeasurement from the first sensor at a temperature within thetemperature range and a pressure within the pressure range will bewithin 10 Pa of the pressure after being adjusted by a pressuremeasurement error estimate determined by the pressure measurement errorfunction.

In accordance with some aspects, wherein the mathematical model isselected such that residual errors associated with the mathematicalmodel and the plurality of different temperature and pressurecombinations are each less than a threshold value of 10 Pa.

In accordance with some aspects, the mathematical model is selected whenresidual errors associated with the mathematical model and the pluralityof different temperature and pressure combinations are less thancorresponding residual errors associated with all other mathematicalmodels of the plurality of mathematical models and the plurality ofdifferent temperature and pressure combinations.

In accordance with some aspects, methods described above are repeatedfor a second sensor, wherein the offset associated with the first sensoris different than the offset associated with the second sensor, andwherein the second sensor is the same model of sensor as the firstsensor.

In accordance with some aspects, methods described above are repeatedfor a second sensor using the same mathematical model selected for thefirst sensor but with different parameters, and wherein the secondsensor is the same model of sensor as the first sensor.

In accordance with some aspects, methods described above are repeatedfor a second sensor using a different mathematical model than themathematical model selected for the first sensor, and wherein the secondsensor is the same model of sensor as the first sensor.

In accordance with some aspects, methods described above are repeatedfor a second sensor, wherein the offset associated with the first sensoris different than the offset associated with the second sensor, andwherein the second sensor is a different model of sensor than the firstsensor.

In accordance with some aspects, methods described above are repeatedfor a second sensor using the same mathematical model selected for thefirst sensor but with different parameters, and wherein the secondsensor is a different model of sensor than the first sensor.

In accordance with some aspects, methods described above are repeatedfor a second sensor using a different mathematical model than themathematical model selected for the first sensor, and wherein the secondsensor is a different model of sensor than the first sensor.

In accordance with some aspects, the mathematical model defines a firstmathematical model related to a first subset of the plurality oftemperature and pressure combinations corresponding to a first sub-rangeof temperatures from the range of temperatures and a first sub-range ofpressures from the range of pressures, and further defines a secondmathematical model related to a second subset of the plurality oftemperature and pressure combinations corresponding to a secondsub-range of temperatures from the range of temperatures and a secondsub-range of pressures from the range of pressures.

In accordance with some aspects, the plurality of different temperatureand pressure combinations includes at least 4 different temperature andpressure combinations, wherein the temperature range includestemperatures between 0 and 60 degrees Celsius, and wherein the pressurerange includes pressures between 72,000 and 107,000 Pa.

By way of example, method(s) and processor(s) may also or alternatively:receive a reported pressure measurement from a pressure sensor.

By way of example, method(s) and processor(s) may also or alternatively:estimate a pressure measurement error by solving a pressure measurementerror function using the reported pressure measurement as an input. Inaccordance with some aspects, the pressure measurement error function isbased on a mathematical model fitted to a plurality of pressuremeasurement errors that each relate to a respective difference between areported measurement of pressure from the pressure sensor after thepressure sensor stabilized to a respective combination of temperatureand pressure, and a calibrated measurement of the pressure from thatrespective combination.

By way of example, method(s) and processor(s) may also or alternatively:obtaining an adjusted pressure measurement for use in determining analtitude of the first sensor by adjusting the reported pressuremeasurement by the estimated pressure measurement error.

In accordance with some aspects, the pressure measurement error functionis further based on a pressure measurement error offset that relates toa difference between a modeled pressure measurement error and a controlpressure measurement error.

In accordance with some aspects, the control pressure measurement erroris based on a difference between another reported measurement ofpressure from the pressure sensor after having stabilized to a controltemperature and a control pressure, and a calibrated measurement of thecontrol pressure.

In accordance with some aspects, the modeled pressure measurement erroris determined by inputting, into the mathematical model, a measurementof the control temperature and the reported measurement of the controlpressure.

In accordance with some aspects, the plurality of different temperatureand pressure combinations are selected so that any reported pressuremeasurement from the first sensor at a temperature within thetemperature range and a pressure within the pressure range will bewithin 10 Pa of the pressure after being adjusted by a pressuremeasurement error determined by the pressure measurement error function.

In accordance with some aspects, the mathematical model is selected suchthat residual errors associated with the mathematical model and theplurality of different temperature and pressure combinations are eachless than a threshold value of 10 Pa

In accordance with some aspects, the mathematical model is selected whenresidual errors associated with the mathematical model and the pluralityof different temperature and pressure combinations are less thancorresponding residual errors associated with all other mathematicalmodels of the plurality of mathematical models and the plurality ofdifferent temperature and pressure combinations

In accordance with some aspects, the mathematical model defines a firstmathematical model related to a first subset of the plurality oftemperature and pressure combinations corresponding to a first sub-rangeof temperatures from the range of temperatures and a first sub-range ofpressures from the range of pressures, and further defines a secondmathematical model related to a second subset of the plurality oftemperature and pressure combinations corresponding to a secondsub-range of temperatures from the range of temperatures and a secondsub-range of pressures from the range of pressures.

Systems may include any or all of: various sensors described herein andknown in the art; one or more receivers at which position information isreceived and used to compute a position of the respective receiver; oneor more servers at which position information is received and used tocompute a position of a receiver; both receivers and servers; or othercomponents.

An output from one system may cause another system to perform a methodeven if intervening steps occur between the output and performance ofthe method.

Any method step or feature disclosed herein may be expressly restrictedfrom a claim for various reasons like achieving reduced manufacturingcosts, lower power consumption, and increased processing efficiency.

The illustrative methods described herein may be implemented, performed,or otherwise controlled by suitable hardware known or later-developed byone of ordinary skill in the art, or by firmware or software executed byprocessor(s), or any combination of hardware, software and firmware.Software may be downloadable and non-downloadable at a particularsystem. Such software comprises a machine-implemented component that,once loaded on a machine like a processor or a computer, changes theoperation of that machine.

Systems on which methods described herein are performed may include oneor more means that implement those methods. For example, such means mayinclude processor(s) or other hardware that, when executing instructions(e.g., embodied in software or firmware), perform any method stepdisclosed herein. A processor may include, or be included within, acomputer or computing device, a controller, an integrated circuit, a“chip”, a system on a chip, a server, other programmable logic devices,other circuitry, or any combination thereof.

“Memory” may be accessible by a machine (e.g., a processor), such thatthe machine can read/write information from/to the memory. Memory may beintegral with or separate from the machine. Memory may include anon-transitory machine-readable medium having machine-readable programcode (e.g., instructions) embodied therein that is adapted to beexecuted to implement each of the methods and method steps disclosedherein. Memory may include any available storage media, includingremovable, non-removable, volatile, and non-volatile media—e.g.,integrated circuit media, magnetic storage media, optical storage media,or any other computer data storage media. As used herein,machine-readable media includes all forms of machine-readable mediaexcept to the extent that such media is deemed to be non-statutory(e.g., transitory propagating signals).

Application programs may carry out aspects by receiving, converting,processing, storing, retrieving, transferring and/or exporting data,which may be stored in a hierarchical, network, relational,non-relational, object-oriented, or other data source. A data source maybe a single storage device or realized by multiple (e.g., distributed)storage devices.

All of the information disclosed herein may be represented by data, andthat data may be transmitted over any communication pathway using anyprotocol, stored on a data source, and processed by a processor. Forexample, transmission of data may be carried out using a variety ofwires, cables, radio signals and infrared light beams, and an evengreater variety of connectors, plugs and protocols even if not shown orexplicitly described. Systems/platforms described herein may exchangeinformation with each other (and with other systems that are notdescribed) using any known or later-developed communication technology,including WiFi, Bluetooth, NFC and other communication networktechnologies. Carrier waves may be used to transfer data andinstructions through electronic, optical, air, electromagnetic, radiofrequency, or other signaling media over a network using networktransfer protocols, including data that is transferred in data signals.Data, instructions, commands, information, signals, bits, symbols, andchips disclosed herein may be represented by voltages, currents,electromagnetic waves, magnetic fields or particles, optical fields orparticles, or any combination thereof.

Different systems disclosed herein may be geographically dispersed fromone another in different regions (e.g., cities, countries), such thatdifferent method steps are performed in different regions and bydifferent systems.

Features in system figures that are illustrated as rectangles may referto hardware, firmware or software, each of which may comprise acomponent of a device. It is noted that lines linking two such featuresmay be illustrative of data transfer between those features. Suchtransfer may occur directly between those features or throughintermediate features even if not illustrated. Where no line connectstwo features, transfer of data between those features is contemplatedunless otherwise stated. Thus, such lines are provided to illustratecertain aspects, but should not be interpreted as limiting. The wordscomprise, comprising, include, including and the like are to beconstrued in an inclusive sense (i.e., not limited to) as opposed to anexclusive sense (i.e., consisting only of). Words using the singular orplural number also include the plural or singular number, respectively.The words or or and, as used in the Detailed Description, cover any ofthe items and all of the items in a list. The words some, any and atleast one refer to one or more. The term may is used herein to indicatean example, not a requirement—e.g., a thing that may perform anoperation or may have a characteristic need not perform that operationor have that characteristic in each embodiment, but that thing performsthat operation or has that characteristic in at least one embodiment.This disclosure is not intended to be limited to the aspects shownherein but is to be accorded the widest scope understood by a skilledartisan, including equivalents.

A user device may be in the form of a cellular or smart phone, a tabletdevice, a PDA, a notebook, a digital camera, an asset tracking tag, anankle bracelet or other device.

Certain aspects disclosed herein relate to a positioning system thatestimates the positions of things—e.g., where the position isrepresented in terms of: latitude, longitude and/or altitudecoordinates; x, y and/or z coordinates; angular coordinates; or otherrepresentations known by one of skill in the art. Positioning systemsuse various techniques to estimate the position of a thing (e.g., areceiver), including trilateration, which is the process of usinggeometry to estimate the position using distances traveled by different“ranging” signals that are received by the receiver from differentbeacons (e.g., transmitters, satellites, antennas). If the transmissiontime and reception time of a ranging signal are known, then thedifference between those times multiplied by speed of light wouldprovide an estimate of the distance traveled by that ranging signal.These estimates of distance are often referred to as “range”measurements. When errors in the measured time(s) are present, a “range”measurement is typically referred to as a “pseudorange” measurement.Thus, a “pseudorange” measurement is a type of “range” measurement.Positioning systems and methods that estimate a position of a receiverbased on signaling from beacons (e.g., transmitters and/or satellites)are described in co-assigned U.S. Pat. No. 8,130,141, issued Mar. 6,2012, and U.S. patent application Ser. No. 13/296,067, filed Nov. 14,2011, which are incorporated herein in their entirety and for allpurposes, except where their content conflicts with the content of thisdisclosure.

RELATED APPLICATIONS

This application relates to U.S. Patent Application Ser. No. 61/899,846,filed Nov. 4, 2013, entitled DETERMINING CALIBRATED MEASUREMENTS OFPRESSURE FOR DIFFERENT SENSORS, the content of which is herebyincorporated by reference herein in its entirety.

1. A computer-implemented method for calibrating a sensor based ondifferent environmental conditions, the method comprising: identifyingoperating parameters, wherein the operating parameters include a set oftemperatures and a set of pressures; for each of a plurality ofdifferent temperature and pressure combinations that use temperaturesfrom the set of temperatures and pressures from the set of pressures,identifying a reported measurement of pressure from a first sensor whenthe first sensor is stabilized to the temperature and the pressure ofthat combination, and computing a pressure measurement error based on acomparison of a calibrated measurement of the pressure and the reportedmeasurement; selecting a mathematical model that fits the computedpressure measurement errors as a function of the reported measurement ofpressure and a measurement of temperature corresponding to each of thetemperature and pressure combinations; and storing a pressuremeasurement error function based on the mathematical model for later usein adjusting pressure measurements from the first sensor.
 2. The methodof claim 1, wherein the method comprising: identifying an additionalreported measurement of pressure from the first sensor when the firstsensor is stabilized to a control temperature and a control pressure;computing a control pressure measurement error based on a comparison ofthe additional reported measurement and a calibrated measurement of thecontrol pressure; computing a modeled pressure measurement error basedon the mathematical model using model inputs that are based on thereported measurement of the control pressure from the first sensor and ameasurement of the control temperature; determining a pressuremeasurement error offset based on a difference between the modeledpressure measurement error and the control pressure measurement error;and wherein the pressure measurement error function is based further onthe pressure measurement error offset.
 3. The method of claim 1, whereinthe plurality of different temperature and pressure combinations areselected so that any reported pressure measurement from the first sensorat a temperature within the set of temperatures and a pressure withinthe set of pressures will be within 10 Pa of the pressure after beingadjusted by a pressure measurement error determined by the pressuremeasurement error function.
 4. The method of claim 1, wherein themathematical model is selected from a plurality of other mathematicalmodels such that residual errors associated with the mathematical modelare each less than a threshold value of 10 Pa.
 5. The method of claim 1,wherein the mathematical model is selected from a plurality of othermathematical models when residual errors associated with themathematical model are less than corresponding residual errorsassociated with all of the other mathematical models.
 6. The method ofclaim 2, wherein the steps of claim 2 are repeated for a second sensor,wherein the offset associated with the first sensor is different thanthe offset associated with the second sensor, and wherein the secondsensor is the same model of sensor as the first sensor.
 7. The method ofclaim 1, wherein the steps of claim 1 are repeated for a second sensorusing the same mathematical model selected for the first sensor but witha different fit of computed pressure measurement errors as a function ofa reported measurement of pressure by the second sensor, and wherein thesecond sensor is the same model of sensor as the first sensor.
 8. Themethod of claim 1, wherein the steps of claim 1 are repeated for asecond sensor using a different mathematical model than the mathematicalmodel selected for the first sensor, and wherein the second sensor isthe same model of sensor as the first sensor.
 9. The method of claim 2,wherein the steps of claim 2 are repeated for a second sensor, whereinthe offset associated with the first sensor is different than the offsetassociated with the second sensor, and wherein the second sensor is adifferent model of sensor than the first sensor.
 10. The method of claim1, wherein the steps of claim 1 are repeated for a second sensor usingthe same mathematical model selected for the first sensor but with adifferent fit of computed pressure measurement errors as a function of areported measurement of pressure by the second sensor, and wherein thesecond sensor is a different model of sensor than the first sensor. 11.The method of claim 1, wherein the steps of claim 1 are repeated for asecond sensor using a different mathematical model than the mathematicalmodel selected for the first sensor, and wherein the second sensor is adifferent model of sensor than the first sensor.
 12. The method of claim1, wherein the mathematical model defines a first model related to afirst subset of the plurality of temperature and pressure combinationscorresponding to a first subset of temperatures from the set oftemperatures and a first subset of pressures from the set of pressures,and further defines a second model related to a second subset of theplurality of temperature and pressure combinations corresponding to asecond subset of temperatures from the set of temperatures and a secondsubset of pressures from the set of pressures.
 13. The method of claim1, wherein the plurality of different temperature and pressurecombinations includes at least 4 different temperature and pressurecombinations, wherein the set of temperatures includes temperaturesbetween 0 and 60 degrees Celsius, and wherein the set of pressuresincludes pressures between 72,000 and 107,000 Pa.
 14. One or moreprocessors that: estimate a pressure measurement error using thepressure measurement error function of claim 1 using a reported pressuremeasurement from the first sensor as an input; and obtaining an adjustedpressure measurement for use in determining an altitude of the firstsensor by adjusting the reported pressure measurement by the estimatedpressure measurement error.
 15. A computer-implemented method fordetermining a pressure measurement error associated with a pressuresensor, the method comprising: receiving a reported pressure measurementfrom a pressure sensor; estimating a pressure measurement error by usingthe reported pressure measurement as an input into a pressuremeasurement error function using, wherein the pressure measurement errorfunction is based on a mathematical model fitted to a plurality ofpressure measurement errors that each relate to a respective differencebetween a reported measurement of pressure from the pressure sensorafter the pressure sensor stabilized to a respective combination oftemperature and pressure, and a calibrated measurement of the pressurefrom that respective combination; and obtaining an adjusted pressuremeasurement for use in determining an altitude of the first sensor byadjusting the reported pressure measurement by the estimated pressuremeasurement error.
 16. The method of claim 15, wherein the pressuremeasurement error function is further based on a pressure measurementerror offset that relates to a difference between a modeled pressuremeasurement error and a control pressure measurement error, wherein thecontrol pressure measurement error is based on a difference betweenanother reported measurement of pressure from the pressure sensor afterhaving stabilized to a control temperature and a control pressure, and acalibrated measurement of the control pressure, and wherein the modeledpressure measurement error is determined by inputting, into themathematical model, a measurement of the control temperature and thereported measurement of the control pressure.
 17. The method of claim15, wherein the plurality of different temperature and pressurecombinations are selected so that any reported pressure measurement fromthe first sensor at a temperature within a set of temperatures and apressure within a set of pressures will be within 10 Pa of the pressureafter being adjusted by a pressure measurement error determined by thepressure measurement error function.
 18. The method of claim 15, whereinthe mathematical model is used such that residual errors associated withthe mathematical model are each less than a threshold value of 10 Pa.19. The method of claim 15, wherein the mathematical model is selectedfrom a plurality of mathematical models when residual errors associatedwith the mathematical model are less than corresponding residual errorsassociated with all other mathematical models of the plurality ofmathematical models.
 20. The method of claim 15, wherein themathematical model defines a first model related to a first subset ofthe plurality of temperature and pressure combinations corresponding toa first subset of temperatures from a set of temperatures and a firstsubset of pressures from a set of pressures, and further defines asecond model related to a second subset of the plurality of temperatureand pressure combinations corresponding to a second subset oftemperatures from the set of temperatures and a second subset ofpressures from the set of pressures.